A bit of behavioral comparison suggests that Giraffes have roughly the same neck posture as other ungulates while drinking and that the horribly awkward stance is due to the legs being very long proportionally, even more so than the neck. As for whether or not Giraffes can bend their necks further down than their drinking posture, yes, they can.

Masai Giraffe (_Giraffa tippelskirchi_) at Roger Williams Park Zoo

As for whether or not this Giraffe managed to get its mouth to the ground and why it would place such a strain on its nuchal ligament, rete mirabile, and who knows what else, I really don’t know. This was a young individual, so perhaps it was just playing around and exploring its limits. I did observe other neck-related wackiness in this individual, but that’s a story for another day, probably tomorrow.